shankar.ashwin wrote:Linda has a wheat business. She purchases wheat from a local wholesaler at a particular cost per pound. The price of the wheat at her stores is $3 per pound. Her faulty spring balance reads 0.9 pounds for a pound. Also, in the festival season, she gives a 10% discount on the wheat. She found that she made neither a profit nor a loss in the festival season. At what price did Linda purchase the wheat from the wholesaler?

A) 2.43
B) 2.5
C) 2.7
D) 3
E) 3.3

Let the purchase price per pound be 'x'
she sold 'n' pounds; for those 'n' pounds, she needs to have purchased 1.1n pounds
(1.1n)*x = (n)*3*0.9
x= 2.45

shankar.ashwin wrote:Linda has a wheat business. She purchases wheat from a local wholesaler at a particular cost per pound. The price of the wheat at her stores is $3 per pound. Her faulty spring balance reads 0.9 pounds for a pound. Also, in the festival season, she gives a 10% discount on the wheat. She found that she made neither a profit nor a loss in the festival season. At what price did Linda purchase the wheat from the wholesaler?

A) 2.43
B) 2.5
C) 2.7
D) 3
E) 3.3

To make the math easier, let the regular selling price per pound = 300.
In registering .9 pounds for every actual pound sold, Linda's scale fails to account for 10% of every pound sold.
The result is that Linda loses 10% of what she should be earning:
300 - .1(300) = 270.
The discount causes Linda to lose another 10%:
270 - .1(270) = 243.
Thus, in order to break even, Linda must pay $243 for the wheat.

The correct answer is A.

CP= SP

also if purchased quantity = 10 then sold quantity = 0.9*10 = 9 units

CP* 10 = 2.7 * 9
CP = 2.43

Cost price of 10 items = Selling price of 9 items

SP after discount = 3*0.9 = 2.7

Therefore, CP of 1 item = 2.7*9/10 = 2.43

shankar.ashwin wrote:Linda has a wheat business. She purchases wheat from a local wholesaler at a particular cost per pound. The price of the wheat at her stores is $3 per pound. Her faulty spring balance reads 0.9 pounds for a pound. Also, in the festival season, she gives a 10% discount on the wheat. She found that she made neither a profit nor a loss in the festival season. At what price did Linda purchase the wheat from the wholesaler?

A) 2.43
B) 2.5
C) 2.7
D) 3
E) 3.3

Guys,

Where am I doing it wrong?

If her balance measures 0.9 for 1.0 then she will have to give 1.1 for a pound. Her selling price is 3 and there is a 10% discount on this. So the selling price becomes 2.7

so for 1.1 pounds she charges 2.7. Hence for 1 pound she will charge 2.7/1.1. This should be her cost price

Please help

Regards,
Vishal

Nothing really wrong with your approach, but you dont get the exact answer because you round off values..

If her balance measures 0.9 for 1.0 then she will have to give 1.1 for a pound.

1/0.9 = 1.111111..

and 2.7/1.111111 ~ 2.43

but 2.7/1.1 ~ 2.45

Refer Mitch's solution to avoid this error. Hope you got it

vishal.pathak wrote:
Guys,

Where am I doing it wrong?

If her balance measures 0.9 for 1.0 then she will have to give 1.1 for a pound. Her selling price is 3 and there is a 10% discount on this. So the selling price becomes 2.7

so for 1.1 pounds she charges 2.7. Hence for 1 pound she will charge 2.7/1.1. This should be her cost price

Please help

Regards,
Vishal

This is how I did it.

Assuming she buys P pounds at c dollars a pound. The price she paid is cP.

Now her selling price is 3(1-10/100) = 2.7 dollars a pound.

Her scale read 0.9 pounds for a pound, so when it read 1 pound the actual weight will be 1/(.9) = 10/9 pounds.

Now the P pounds she bought is split in 10/9 portions and each portion [P / (10/9) = P * (9/10)] is sold at 2.7 dollars per portion (she thinks each portion is actually a pound).

Total cost = cP
Total revenue from sales = 2.7 * [(9/10) * P]

She breaks even => cP = 2.7 * [(9/10) * P]

Cancelling P out, c = 2.43.

Hope that helps.